6.2 Using the Normal Distribution — Statistics

6.2 Exercise 1

If the area to the left of x is 0.012, then what is the area to the right?

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6.2 Exercise 3

The final exam scores in a statistics class were normally distributed with a mean of 63 and a standard deviation of five.

b. Find the probability that a randomly selected student scored less than 85.

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6.2 Exercise 5

d. Find the 70^th percentile, that is, find the score k such that 70 percent of scores are below k and 30 percent of the scores are above k.

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6.2 Exercise 6

The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three.

Find the probability that a randomly selected golfer scored less than 65.

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6.2 Exercise 9

The golf scores for a school team were normally distributed with a mean of 68 and a standard deviation of three. Find the probability that a golfer scored between 66 and 70.

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6.2 Exercise 10

In the United States smartphone users between the ages of 13 and 55+ approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively.

a. Determine the probability that a random smartphone user in the age range 13 to 55+ is between 23 and 64.7 years old.

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6.2 Exercise 11

In the United States smartphone users between the ages of 13 and 55+ approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively.

b. Determine the probability that a randomly selected smartphone user in the age range 13 to 55+ is at most 50.8 years old.

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6.2 Exercise 12

In the United States smartphone users between the ages of 13 and 55+ approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively.

c. Find the 80^th percentile of this distribution, and interpret it in a complete sentence.

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6.2 Exercise 14

In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively. Using this information, answer the following questions. Round answers to one decimal place.

a. Calculate the interquartile range (IQR).

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6.2 Exercise 15

In the United States the ages 13 to 55+ of smartphone users approximately follow a normal distribution with approximate mean and standard deviation of 36.9 years and 13.9 years, respectively. Using this information, answer the following questions. Round answers to one decimal place.

b. Forty percent of the ages that range from 13 to 55+ are at least what age?

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6.2 Exercise 16

Two thousand students took an exam. The scores on the exam have an approximate normal distribution with a mean μ = 81 points and standard deviation σ = 15 points.

Calculate the first- and third-quartile scores for this exam.
The middle 50 percent of the exam scores are between what two values?

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6.2 Exercise 18

A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal distribution with a mean diameter of 5.85 cm and a standard deviation of 0.24 cm.

b. The middle 20 percent of mandarin oranges from this farm have diameters between ______ and ______.

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6.2 Exercise 19

A citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal distribution with a mean diameter of 5.85 cm and a standard deviation of 0.24 cm.

c. Find the 90^th percentile for the diameters of mandarin oranges, and interpret it in a complete sentence.

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6.2 Exercise 20

Using the information from the example, answer the following:

The middle 45 percent of mandarin oranges from this farm are between ______ and ______.
Find the 16^th percentile, and interpret it in a complete sentence.

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6.2 Exercise 23

Is P(x < 1) equal to P(x ≤ 1)? Why or why not?

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6.2 Exercise 27

If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x?

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6.2 Exercise 29

X ~ N(54, 8)

Find the probability that x < 30.

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6.2 Exercise 31

X ~ N(54, 8)

Find the 60^th percentile.

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6.2 Exercise 33

X ~ N(54, 8)

X ~ N(–3, 4)

Find the probability that x is between one and four.

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6.2 Exercise 39

Use the following information to answer the next two exercises: The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of 2.1 days.

The 90^th percentile for recovery times is –

8.89
7.07
7.99
4.32

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